Unitary precoding based on randomized FFT matrices

ABSTRACT

Systems and methodologies are described that facilitate constructing unitary matrices that may be utilized in linear precoding for multiple-input multiple-output (MIMO) wireless communication systems. Each unitary matrix may be generated by combining (e.g., multiplying) a diagonal matrix with a Discrete Fourier Transform (DFT) matrix. The unitary matrices may be utilized to provide feedback related to a channel and/or control transmission over a channel based upon obtained feedback.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a divisional application of U.S. patentapplication Ser. No. 11/553,462, filed on Oct. 26, 2006, titled “UNITARYPRECODING BASED ON RANDOMIZED FFT MATRICES” which claims the benefit toU.S. Provisional Patent Application No. 60/731,301, filed Oct. 28, 2005,titled “A METHOD AND APPARATUS FOR PRE-CODING”. The entireties of theaforementioned applications are herein incorporated by reference.

BACKGROUND

I. Field

The following description relates generally to wireless communications,and more particularly to generating unitary matrices that can beutilized in connection with linear precoding in a wireless communicationsystem.

II. Background

Wireless communication systems are widely deployed to provide varioustypes of communication content such as, for example, voice, data, and soon. Typical wireless communication systems may be multiple-accesssystems capable of supporting communication with multiple users bysharing available system resources (e.g., bandwidth, transmit power, . .. ). Examples of such multiple-access systems may include code divisionmultiple access (CDMA) systems, time division multiple access (TDMA)systems, frequency division multiple access (FDMA) systems, orthogonalfrequency division multiple access (OFDMA) systems, and the like.

Generally, wireless multiple-access communication systems maysimultaneously support communication for multiple mobile devices. Eachmobile device may communicate with one or more base stations viatransmissions on forward and reverse links. The forward link (ordownlink) refers to the communication link from base stations to mobiledevices, and the reverse link (or uplink) refers to the communicationlink from mobile devices to base stations. Further, communicationsbetween mobile devices and base stations may be established viasingle-input single-output (SISO) systems, multiple-input single-output(MISO) systems, multiple-input multiple-output (MIMO) systems, and soforth.

MIMO systems commonly employ multiple (N_(T)) transmit antennas andmultiple (N_(R)) receive antennas for data transmission. A MIMO channelformed by the N_(T) transmit and N_(R) receive antennas may bedecomposed into N_(S) independent channels, which may be referred to asspatial channels, where N_(S)≦{N_(T),N_(R)}. Each of the N_(S)independent channels corresponds to a dimension. Moreover, MIMO systemsmay provide improved performance (e.g., increased spectral efficiency,higher throughput and/or greater reliability) if the additionaldimensionalities created by the multiple transmit and received antennasare utilized.

MIMO systems may support various duplexing techniques to divide forwardand reverse link communications over a common physical medium. Forinstance, frequency division duplex (FDD) systems may utilize disparatefrequency regions for forward and reverse link communications. Further,in time division duplex (TDD) systems, forward and reverse linkcommunications may employ a common frequency region. However,conventional techniques may provide limited or no feedback related tochannel information. Further, transmissions over a channel oftentimesfail to be tailored based upon conditions and/or properties of thechannel.

SUMMARY

The following presents a simplified summary of one or more embodimentsin order to provide a basic understanding of such embodiments. Thissummary is not an extensive overview of all contemplated embodiments,and is intended to neither identify key or critical elements of allembodiments nor delineate the scope of any or all embodiments. Its solepurpose is to present some concepts of one or more embodiments in asimplified form as a prelude to the more detailed description that ispresented later.

In accordance with one or more embodiments and corresponding disclosurethereof, various aspects are described in connection facilitatingconstruction of unitary matrices that may be utilized in linearprecoding for multiple-input multiple-output (MIMO) wirelesscommunication systems. Each unitary matrix may be generated by combining(e.g., multiplying) a diagonal matrix with a Discrete Fourier Transform(DFT) matrix. The unitary matrices may be utilized to provide feedbackrelated to a channel and/or control transmission over a channel basedupon obtained feedback.

According to related aspect, a method that facilitates providing channelrelated feedback for precoding in a wireless communication system isdescribed herein. The method may comprise constructing a set of unitarymatrices, each of the unitary matrices being generated based upon adiagonal matrix and a Discrete Fourier Transform (DFT) matrix. Further,the method may include selecting a particular unitary matrix from theset of unitary matrices based upon an estimate of a forward linkchannel. Moreover, the method may comprise transmitting an indexassociated with the particular unitary matrix via a reverse linkchannel.

Another aspect relates to a wireless communications apparatus. Thewireless communications apparatus may include a memory that retainsinstructions for generating a set of unitary matrices based upon acombination of diagonal matrices and Discrete Fourier Transform (DFT)matrices and yielding channel related feedback for precoding selectedfrom the set of unitary matrices. Further, the communications apparatusmay comprise a processor, coupled to the memory, configured to executethe instructions retained in the memory.

Yet another aspect relates to a wireless communications apparatus thatgenerates unitary matrices and provides channel related feedback forprecoding. The wireless communications apparatus may include means forconstructing a set of unitary matrices based upon diagonal matrices andDiscrete Fourier Transform (DFT) matrices; means for selecting aparticular unitary matrix from the set of unitary matrices based upon achannel estimate; and means for transmitting an index associated withthe particular unitary matrix via a reverse link channel.

Still another aspect relates to a machine-readable medium having storedthereon machine-executable instructions for generating a set of unitarymatrices, each of the unitary matrices being constructed as a functionof a diagonal matrix and a Discrete Fourier Transform (DFT) matrix,estimating a forward link channel to yield a channel estimate, andidentifying a particular unitary matrix from the set of unitary matricesbased upon the channel estimate. The machine-readable medium may furtherhave stored thereon machine-executable instructions for determining anindex of the particular unitary matrix selected from the set of unitarymatrices and transmitting the index via a reverse link channel.

In accordance with another aspect, an apparatus in a wirelesscommunication system may include a processor, wherein the processor maybe configured to generate a codebook of unitary matrices based upondiagonal matrices and Discrete Fourier Transform (DFT) matrices.Further, the processor may be configured to determine a particularunitary matrix to feedback for utilization in precoding based upon anevaluation of a forward link channel. Moreover, the processor may beconfigured to send an index associated with the particular unitarymatrix to a base station via a reverse link channel.

According to a further aspect, a method that facilitates controllingtransmission in response to feedback in a wireless communication systemis described herein. The method may comprise constructing a set ofunitary matrices, each of the unitary matrices being generated basedupon a diagonal matrix and a Discrete Fourier Transform (DFT) matrix.Further, the method may include identifying a selected unitary matrixfrom the set of unitary matrices based upon a received index.Additionally, the method may include modifying transmission over aforward link channel based upon the selected unitary matrix.

Another aspect relates to a wireless communications apparatus. Thewireless communications apparatus may include a memory that retainsinstructions for constructing a set of unitary matrices based upon acombination of diagonal matrices and Discrete Fourier Transform (DFT)matrices, identifying a particular unitary matrix from the set basedupon an obtained index, and controlling transmission over a forward linkchannel based upon the particular unitary matrix. Further, the wirelesscommunications apparatus may include a processor, coupled to the memory,configured to execute the instructions retained in memory.

Still another aspect relates to a wireless communications apparatus thatconstructs unitary matrices and controls transmission over a channel.The wireless communications apparatus may include means for generating aset of unitary matrices based upon diagonal matrices and DiscreteFourier Transform (DFT) matrices, means for identifying a selectedunitary matrix from the set of unitary matrices based upon a receivedindex, and means for controlling transmission over a forward linkchannel based upon the selected unitary matrix.

Yet another aspect relates to a machine-readable medium having storedthereon machine-executable instructions for obtaining a diagonal matrix;obtaining a Discrete Fourier Transform (DFT) matrix; and combining thediagonal matrix and the DFT matrix to yield a unitary matrix utilized inconnection with linear precoding.

In accordance with another aspect, an apparatus in a wirelesscommunication system may include a processor, wherein the processor maybe configured to build a codebook that includes a set of unitarymatrices based upon diagonal matrices and Discrete Fourier Transform(DFT) matrices, determine a selected unitary matrix from the set ofunitary matrices based upon a received index, and adapt transmissionover a forward link channel based upon the selected unitary matrix.

To the accomplishment of the foregoing and related ends, the one or moreembodiments comprise the features hereinafter fully described andparticularly pointed out in the claims. The following description andthe annexed drawings set forth in detail certain illustrative aspects ofthe one or more embodiments. These aspects are indicative, however, ofbut a few of the various ways in which the principles of variousembodiments may be employed and the described embodiments are intendedto include all such aspects and their equivalents.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an illustration of a wireless communication system inaccordance with various aspects set forth herein.

FIG. 2 is an illustration of an example communications apparatus foremployment within a wireless communications environment.

FIG. 3 is an illustration of an example system that effectuates unitaryprecoding in a wireless communication environment.

FIG. 4 is an illustration of an example methodology that facilitatesyielding one or more unitary matrices that may be utilized in linearprecoding in a MIMO wireless communication system.

FIG. 5 is an illustration of an example methodology that facilitatesproviding channel related feedback by leveraging a set of constructedunitary matrices in a MIMO wireless communication system.

FIG. 6 is an illustration of an example methodology that facilitatescontrolling transmission over a forward link channel based upon aunitary matrix in a MIMO wireless communication system.

FIG. 7 is an illustration of an example mobile device that facilitatesgenerating a set of unitary matrices that may be employed in linearprecoding for a MIMO wireless communication system.

FIG. 8 is an illustration of an example system that facilitatesgenerating unitary matrices and/or utilizing unitary matricesconstructed based at least in part upon randomized DFT matrices inconnection with linear precoding in a MIMO wireless communicationsystem.

FIG. 9 is an illustration of an example wireless network environmentthat can be employed in conjunction with the various systems and methodsdescribed herein.

FIG. 10 is an illustration of an example system that generates unitarymatrices and provides channel related feedback by leveraging the unitarymatrices in a MIMO wireless communication environment.

FIG. 11 is an illustration of an example system that constructs unitarymatrices and controls transmission over a channel by employing theunitary matrices in a MIMO wireless communication environment.

DETAILED DESCRIPTION

Various embodiments are now described with reference to the drawings,wherein like reference numerals are used to refer to like elementsthroughout. In the following description, for purposes of explanation,numerous specific details are set forth in order to provide a thoroughunderstanding of one or more embodiments. It may be evident, however,that such embodiment(s) may be practiced without these specific details.In other instances, well-known structures and devices are shown in blockdiagram form in order to facilitate describing one or more embodiments.

As used in this application, the terms “component,” “module,” “system,”and the like are intended to refer to a computer-related entity, eitherhardware, firmware, a combination of hardware and software, software, orsoftware in execution. For example, a component may be, but is notlimited to being, a process running on a processor, a processor, anobject, an executable, a thread of execution, a program, and/or acomputer. By way of illustration, both an application running on acomputing device and the computing device can be a component. One ormore components can reside within a process and/or thread of executionand a component may be localized on one computer and/or distributedbetween two or more computers. In addition, these components can executefrom various computer readable media having various data structuresstored thereon. The components may communicate by way of local and/orremote processes such as in accordance with a signal having one or moredata packets (e.g., data from one component interacting with anothercomponent in a local system, distributed system, and/or across a networksuch as the Internet with other systems by way of the signal).

Furthermore, various embodiments are described herein in connection witha mobile device. A mobile device can also be called a system, subscriberunit, subscriber station, mobile station, mobile, remote station, remoteterminal, access terminal, user terminal, terminal, wirelesscommunication device, user agent, user device, or user equipment (UE). Amobile device may be a cellular telephone, a cordless telephone, aSession Initiation Protocol (SIP) phone, a wireless local loop (WLL)station, a personal digital assistant (PDA), a handheld device havingwireless connection capability, computing device, or other processingdevice connected to a wireless modem. Moreover, various embodiments aredescribed herein in connection with a base station. A base station maybe utilized for communicating with mobile device(s) and may also bereferred to as an access point, Node B, or some other terminology.

Moreover, various aspects or features described herein may beimplemented as a method, apparatus, or article of manufacture usingstandard programming and/or engineering techniques. The term “article ofmanufacture” as used herein is intended to encompass a computer programaccessible from any computer-readable device, carrier, or media. Forexample, computer-readable media can include but are not limited tomagnetic storage devices (e.g., hard disk, floppy disk, magnetic strips,etc.), optical disks (e.g., compact disk (CD), digital versatile disk(DVD), etc.), smart cards, and flash memory devices (e.g., EPROM, card,stick, key drive, etc.). Additionally, various storage media describedherein can represent one or more devices and/or other machine-readablemedia for storing information. The term “machine-readable medium” caninclude, without being limited to, wireless channels and various othermedia capable of storing, containing, and/or carrying instruction(s)and/or data.

Referring now to FIG. 1, a wireless communication system 100 isillustrated in accordance with various embodiments presented herein.System 100 comprises a base station 102 that may include multipleantenna groups. For example, one antenna group may include antennas 104and 106, another group may comprise antennas 108 and 110, and anadditional group may include antennas 112 and 114. Two antennas areillustrated for each antenna group; however, more or fewer antennas maybe utilized for each group. Base station 102 may additional include atransmitter chain and a receiver chain, each of which can in turncomprise a plurality of components associated with signal transmissionand reception (e.g., processors, modulators, multiplexers, demodulators,demultiplexers, antennas, etc.), as will be appreciated by one skilledin the art.

Base station 102 may communicate with one or more mobile devices such asmobile device 116 and mobile device 122; however, it is to beappreciated that base station 102 may communicate with substantially anynumber of mobile devices similar to mobile devices 116 and 122. Mobiledevices 116 and 122 can be, for example, cellular phones, smart phones,laptops, handheld communication devices, handheld computing devices,satellite radios, global positioning systems, PDAs, and/or any othersuitable device for communicating over wireless communication system100. As depicted, mobile device 116 is in communication with antennas112 and 114, where antennas 112 and 114 transmit information to mobiledevice 116 over a forward link 118 and receive information from mobiledevice 116 over a reverse link 120. Moreover, mobile device 122 is incommunication with antennas 104 and 106, where antennas 104 and 106transmit information to mobile device 122 over a forward link 124 andreceive information from mobile device 122 over a reverse link 126. In afrequency division duplex (FDD) system, forward link 118 may utilize adifferent frequency band than that used by reverse link 120, and forwardlink 124 may employ a different frequency band than that employed byreverse link 126, for example. Further, in a time division duplex (TDD)system, forward link 118 and reverse link 120 may utilize a commonfrequency band and forward link 124 and reverse link 126 may utilize acommon frequency band.

Each group of antennas and/or the area in which they are designated tocommunicate may be referred to as a sector of base station 102. Forexample, antenna groups may be designed to communicate to mobile devicesin a sector of the areas covered by base station 102. In communicationover forward links 118 and 124, the transmitting antennas of basestation 102 may utilize beamforming to improve signal-to-noise ratio offorward links 118 and 124 for mobile devices 116 and 122. Also, whilebase station 102 utilizes beamforming to transmit to mobile devices 116and 122 scattered randomly through an associated coverage, mobiledevices in neighboring cells may be subject to less interference ascompared to a base station transmitting through a single antenna to allits mobile devices.

According to an example, system 100 may be a multiple-inputmultiple-output (MIMO) communication system. Further, system 100 mayutilize any type of duplexing such as FDD, TDD, etc. Pursuant to anillustration, base station 102 may transmit over forward links 118 and124 to mobile devices 116 and 122. Moreover, mobile devices 116 and 122may estimate respective forward link channels and generate correspondingfeedback that may be provided to base station 102 via reverse links 120and 122. Linear precoding techniques may be effectuated (e.g., by basestation 102) based upon the channel related feedback; thus, subsequenttransmissions over the channel may be controlled by utilizing thechannel related feedback (e.g., beamforming gain may be obtained byemploying linear precoding).

Base station 102 and mobile devices 116 and 122 may employ commoncodebooks to provide and/or analyze feedback (e.g., quantize estimatedchannel(s)). The codebooks may each include a set of N unitary matrices,where N may be any integer. For instance, the common codebooks shared bybase station 102 and mobile device 116 (and/or mobile device 122) mayinclude N=2^(M) unitary matrices, where M may be the number of bitsfeedback from a receiver (e.g., mobile device(s) 116 and 122) to atransmitter (e.g., base station 102) to index the precoding matrix.Pursuant to an example, base station 102 and/or mobile devices 116 and122 may construct the unitary matrices of the codebooks. Additionally oralternatively, the unitary matrices may be constructed and distributedto base station 102 and/or mobile devices 116 and 122.

According to an illustration, mobile devices 116 and 122 may estimateforward link channels (e.g., to yield a channel matrix) and compare thechannel estimates with unitary matrices included in the codebooks toselect particular unitary matrices (e.g., closest) from the codebooks(e.g., to quantize the unitary part of the channel matrix). Thereafter,indices associated with the selected unitary matrices may be transmittedto base station 102. Base station 102 may employ the received indices toidentify the selected unitary matrices, which may be utilized to controlcommunication over forward links 118 and 124 (e.g., for beamforming). Byemploying the unitary matrices as described herein, transmission powerof each transmit antenna may be substantially equal regardless of anumber of streams transmitted.

Turning to FIG. 2, illustrated is a communications apparatus 200 foremployment within a wireless communications environment. Communicationsapparatus 200 may be a base station or a portion thereof or a mobiledevice or a portion thereof. Communications apparatus 200 may include aunitary matrix generator 202 that constructs unitary matrices that canbe utilized in connection with linear precoding. For instance, theunitary matrices may be utilized in a MIMO wireless communicationssystem. Moreover, the unitary matrices yielded by unitary matrixgenerator 202 may form a codebook, which may be substantially similar toa codebook of a disparate communications apparatus with whichcommunications apparatus 200 interacts. Although not depicted, it iscontemplated that unitary matrix generator 202 may be separate fromcommunications apparatus 200; according to this example, unitary matrixgenerator 202 may construct and transfer the unitary matrices tocommunications apparatus 200. Pursuant to another example,communications apparatus 200 may construct a codebook of unitarymatrices with unitary matrix generator 202 and thereafter provide theconstructed codebook to a disparate communications apparatus; however,is it to be appreciated that the claimed subject matter is not solimited to the aforementioned examples.

By way of example, communications apparatus 200 may be a base stationthat constructs a codebook of unitary matrices with unitary matrixgenerator 202. The base station may obtain an index related to thecodebook of unitary matrices from a mobile device, where the index maybe selected from a substantially similar codebook of unitary matricesassociated with the mobile device. Additionally or alternatively,communications apparatus 200 may be a mobile device that generates acodebook of unitary matrices by leveraging unitary matrix generator 202.According to this illustration, the mobile device may estimate a channeland utilize the unitary matrices to quantize the channel estimate. Forinstance, a particular unitary matrix that corresponds to the channelestimate may be selected from the set of unitary matrices yielded byunitary matrix generator 202 and an index that pertains to the selectedunitary matrix may be transmitted to a base station (e.g., that employsa substantially similar codebook including a substantially similar setof unitary matrices).

Unitary matrix generator 202 may yield unitary matrices for utilizationin TDD wireless communications systems, FDD wireless communicationssystems, and the like. Unitary matrix generator 202 may construct a setof unitary matrices such as {U_(k)}_(k=1) ^(N), where N may be anyinteger. Further, N=2^(M), where M may be a number of bits of feedback.Pursuant to an example, N may be 64 and accordingly 6 bits of feedback(e.g., associated with an index) may be transferred from a receiver(e.g., mobile device) to a transmitter (e.g., base station); however,the claimed subject matter is not limited to the aforementioned example.

Unitary matrix generator 202 may generate and/or obtain a diagonalmatrix and a Discrete Fourier Transform (DFT) matrix. Further, unitarymatrix generator 202 may construct each of the unitary matrices bymultiplying a DFT matrix by a diagonal matrix. According to anillustration, the diagonal matrix may be associated with a random phase.For example, unitary matrix generator 202 may evaluate

${U_{k} = {\begin{bmatrix}{\mathbb{e}}^{{j2\pi}\;\phi_{k,1}} & \ldots & 0 \\\vdots & \ddots & \vdots \\0 & \ldots & {\mathbb{e}}^{{j2\pi}\;\phi_{k,M_{T}}}\end{bmatrix}F_{M_{T} \times L}\mspace{14mu}{or}}}\mspace{14mu}$${U_{k} = {F_{M_{T} \times L}\begin{bmatrix}{\mathbb{e}}^{{j2\pi}\;\phi_{k,1}} & \ldots & 0 \\\vdots & \ddots & \vdots \\0 & \ldots & {\mathbb{e}}^{{j2\pi}\;\phi_{k,L}}\end{bmatrix}}}\mspace{14mu}$to determine the unitary matrices, where M_(T) may be a number oftransmit antennas and L may be a rank and/or number of space-time codes(e.g., spatial multiplexing streams). Further, {φ_(i)}_(i=1) ^(M) ^(T)be random variables in (0,1), and columns of F may be orthonormal andchosen from columns of a DFT matrix.

According to a further illustration, unitary matrix generator 202 mayevaluate the DFT matrix such as

${F_{M_{T} \times L} = {\frac{1}{\sqrt{M_{T}}}\left\lbrack {\mathbb{e}}^{\frac{{- j}\; 2\;\pi\; n\; l}{M_{T}}} \right\rbrack}},$where n may be from 0 to M_(T)−1 and 1 may be from 0 to L−1. Pursuant toan example where 4 transmit antennas are employed (e.g., by a basestation) and 2 receive antennas are utilized (e.g., by a mobile device),M_(T) may be equal to 4 and L may be equal to 2. In accordance with thisexample, unitary matrix generator 202 may generate a DFT matrix such as

${F_{M_{T} \times L} = {\frac{1}{2}\begin{bmatrix}1 & 1 \\1 & {- j} \\1 & {- 1} \\1 & j\end{bmatrix}}},$and unitary matrix generator 202 may multiply this DFT matrix by thediagonal matrix to yield a unitary matrix

$U_{K} = {\begin{bmatrix}u_{11} & u_{12} \\u_{21} & u_{22} \\u_{31} & u_{32} \\u_{41} & u_{42}\end{bmatrix}.}$

Moreover, although not shown, it is to be appreciated thatcommunications apparatus 200 may include memory that retains variousinstructions with respect to generating unitary matrices, yieldingchannel related feedback based upon unitary matrices, employing feedbackassociated with unitary matrices (e.g., to control subsequenttransmission over a channel), and the like. Further, communicationsapparatus 200 may include a processor that may be utilized in connectionwith executing the instructions (e.g., instructions retained withinmemory, instructions obtained from a disparate source, . . . ).

Now referring to FIG. 3, illustrated is a system 300 that effectuatesunitary precoding in a wireless communication environment. System 300includes a base station 302 that communicates with a mobile device 304(and/or any number of disparate mobile devices (not shown)). Basestation 302 may transmit information to mobile device 304 over a forwardlink channel; further, base station 302 may receive information frommobile device 304 over a reverse link channel. Further, system 300 maybe a MIMO system. According to an example, mobile device 304 may providefeedback related to the forward link channel via the reverse linkchannel, and base station 302 may utilize the feedback to control and/ormodify subsequent transmission over the forward link channel (e.g.,employed to facilitate beamforming).

Mobile device 304 may include a unitary matrix generator 306 thatconstructs unitary matrices by multiplying diagonal matrices by DFTmatrices as described above. Further, base station 302 may include aunitary matrix generator 308 that may be substantially similar tounitary matrix generator 306. Accordingly, base station 302 and mobiledevice 304 may obtain substantially similar codebooks that include acommon set of unitary matrices yielded by unitary matrix generators 306and 308. Although not depicted, it is to contemplated that unitarymatrix generator 306 may construct the codebook for mobile device 304,and the codebook may be provided to base station 302, for example.Pursuant to another illustration, unitary matrix generator 308 may yieldthe codebook for base station 302, which may transfer the codebook tomobile device 304. Moreover, a disparate apparatus may generate thecodebook of unitary matrices and provide the codebook to both basestation 302 and mobile device 304; however, the claimed subject matteris not limited to the aforementioned examples.

Mobile device 304 may further include a channel estimator 310 and afeedback generator 312. Channel estimator 310 may estimate the forwardlink channel from base station 302 to mobile device 304. Channelestimator 310 may generate a matrix H that corresponds to the forwardlink channel, where columns of H may relate to transmit antennas of basestation 302 and rows of H may pertain to receive antennas at mobiledevice 304. According to an example, base station 302 may utilize fourtransmit antennas and mobile device 304 may employ two receive antennas,and thus, channel estimator 310 may evaluate the forward link channel toyield a two-by-four channel matrix H (e.g., where

$\left. {H = \begin{bmatrix}h_{11} & h_{12} & h_{13} & h_{14} \\h_{21} & h_{22} & h_{23} & h_{24}\end{bmatrix}} \right);$however, it is to be appreciated that the claimed subject mattercontemplates utilizing any size (e.g., any number of rows and/orcolumns) channel matrix H (e.g., corresponding to any number of receiveand/or transmit antennas).

Feedback generator 312 may employ the channel estimate (e.g., channelmatrix H) to yield feedback that may be transferred to base station 302over the reverse link channel. According to an example, feedbackgenerator 312 (and/or channel estimator 310) may effectuate eigendecomposition of the channel matrix H to yield a corresponding channelunitary matrix U. For instance, the channel unitary matrix U may includeinformation related to direction of the channel determined from theestimated channel matrix H. Eigen decomposition of the channel matrix Hmay be effectuated based upon H^(H)H=U^(H)ΛU, where U may be a channelunitary matrix corresponding to the channel matrix H, H^(H) may be theconjugate transpose of H, U^(H) may be the conjugate transpose of U, andΛ may be a diagonal matrix.

Moreover, feedback generator 312 may compare the channel unitary matrixU to the set of unitary matrices constructed via unitary matrixgenerator 306 (e.g., to quantize the channel unitary matrix U). Further,a selection may be made from the set of unitary matrices. An indexassociated with the selected unitary matrix from the set may beidentified by feedback generator 312. Moreover, feedback generator 312may provide the index to base station 302 via the reverse link channel.

Base station 302 may further include a feedback evaluator 314 and aprecoder 316. Feedback evaluator 314 may analyze the feedback (e.g., theobtained index associated with the quantized information) received frommobile device 304. For example, feedback evaluator 314 may utilize thecodebook of unitary matrices generated by unitary matrix generator 308to identify the selected unitary matrix based upon the received index;thus, the unitary matrix identified by feedback evaluator 314 may besubstantially similar to the unitary matrix selected by feedbackgenerator 312.

Further, precoder 316 may be utilized by base station 302 to altersubsequent transmissions over the forward link channel based upon theunitary matrix identified by feedback evaluator 314. For example,precoder 316 may perform beamforming for forward link communicationsbased upon the feedback. According to a further example, precoder 316may multiply the identified unitary matrix by a transmit vectorassociated with the transmit antennas of base station 302. Further,transmission power for each transmit antenna employing a unitary matrixconstructed as described herein (e.g., by unitary matrix generators 306and 308) may be substantially similar (as opposed to conventionaltechniques that may utilize a randomly generated unitary matrix that maylead to antennas utilizing disparate power levels).

According to an example, precoding and space division multiple access(SDMA) Codebooks Precoding and SDMA may be a mapping between effectiveantennas and tile antennas. A particular mapping may be defined by aprecoding matrix. The columns of the precoding matrix may define a setof spatial beams that can be used by base station 302. Base station 302may utilize one column of the precoding matrix in SISO transmission, andmultiple columns in STTD or MIMO transmissions.

Mobile device 304 may choose to feedback a preferred precoding matrix tobe used by base station 302 for future transmissions. The set of suchprecoding matrices forms a codebook. A number of example precoding/SDMAcodebooks are described herein and corresponding values ofBFCHBeamCodeBookIndex may be defined in an Overhead Messages protocol.It is to be appreciated that the claimed subject matter is not limitedto the following examples. Some of the precoding matrices in a codebookmay be grouped into clusters. Matrices in a single cluster may span apart of the space. If mobile device 304 feeds back a beam index within acluster, base station 302 treats this as an indication that it mayschedule other mobile devices on different clusters.

A BeamIndex field, in a BFCHBeamIndex report, may index a beam in acodebook specified by BFCHBeamCodeBookIndex. The BeamIndex may indicateone or more of the following: A no preferred precoding or SDMA matrix, apreferred SISO precoding or SDMA transmission on a spatial beam, apreferred STTD precoding or SDMA transmission on two spatial beams, anda preferred MIMO precoding or SDMA transmission on a set of spatialbeams (more than one column of the precoding matrix).

It may be understood that, if the codebook supports MIMO, the 0^(th) to(SpatialOrder−1)^(th) columns of the precoding matrix may be used, whereSpatialOrder is defined in the Forward Traffic Channel MAC protocol. Ifa spatial beam

w = ⌊w₀  w₁  …  w_(N_(EFT_TX_ANT) − 1)⌋^(T),is used to transmit a modulation symbol s, then w_(j)s is transmitted oneffective antenna j, where N_(EFT) _(—) _(TX) _(—) _(ANT) is equal tothe parameter EffectiveNumAntenna maintained in the overhead messagesprotocol, and T is the matrix transpose.

In the sequel i may indicate the imaginary part in a complex number.

BFCHBeamCodeBookIndex=0000. This codebook may be valid for SISOtransmission and N_(EFT) _(—) _(TX) _(—) _(ANT)=4. BeamIndex=0: Mobiledevice 304 does not prefer a specific precoding matrix and ratherprefers a random matrix that is chosen by base station 302. The randommatrix may change at a rate chosen by base station 302.

Cluster 1. BeamIndex=1: [0.5 0.5i −0.5 −0.5i]^(T)

Cluster 2. BeamIndex=2: [0.5 −0.5i −0.5 0.5i]^(T)

BFCHBeamCodeBookIndex=0001. In an aspect, a codebook may be valid forSISO and MIMO transmissions if N_(EFT) _(—) _(TX) _(—) _(ANT)=4.

${{Let}\mspace{14mu}{BeamMat}} = \begin{bmatrix}0.5000 & 0.5000 & 0.5000 & 0.5000 \\{0.3536 + {0.3536\mspace{11mu}{\mathbb{i}}}} & {{- 0.3536} + {0.3536\mspace{11mu}{\mathbb{i}}}} & {0.3536 - {0.3536\mspace{11mu}{\mathbb{i}}}} & {{- 0.3536} - {0.3536\mspace{11mu}{\mathbb{i}}}} \\{0.0000 + {0.5000\mspace{11mu}{\mathbb{i}}}} & {{- 0.0000} - {0.5000\mspace{11mu}{\mathbb{i}}}} & {0.0000 - {0.5000\mspace{11mu}{\mathbb{i}}}} & {{- 0.0000} + {0.5000\mspace{11mu}{\mathbb{i}}}} \\{{- 0.3536} + {0.3536\mspace{11mu}{\mathbb{i}}}} & {0.3536 + {0.3536\mspace{11mu}{\mathbb{i}}}} & {{- 0.3536} - {0.3536\mspace{11mu}{\mathbb{i}}}} & {0.3536 - {0.3536\mspace{11mu}{\mathbb{i}}}}\end{bmatrix}$

The codebook may be defined as follows:

BeamIndex=0: Mobile device 304 does not prefer a specific precodingmatrix and rather prefers a random matrix that is chosen by base station302. The random matrix may change at a rate chosen by base station 302.It should be understood that the above numerical values are provided asan example, and the claimed subject matter is not so limited.

BeamIndex=1: Zero^(th) column in BeamMat

BeamIndex=2: First column in BeamMat

BeamIndex=3: Second column in BeamMat

BeamIndex=4: Third column in BeamMat

Precoding Matrices. According to an example, BeamIndex=5 toBeamIndex=35: If the BeamIndex is equal to j, defineseed_(k,j)=(2π[BIT_REVERSE([4*j+k)*26544357611] mod 2³²)] mod 2²⁰)/2²⁰,k=0,1,2,3. The corresponding precoding matrix, U_(j), may be a randomunitary matrix defined as U_(j)=Λ_(j)D, where Λ_(j) is a diagonal matrixof the form

$\begin{bmatrix}{\mathbb{e}}^{{\mathbb{i}}\;\phi_{0}} & 0 & 0 & 0 \\0 & {\mathbb{e}}^{{\mathbb{i}\phi}_{1}} & 0 & 0 \\0 & 0 & {\mathbb{e}}^{{\mathbb{i}\phi}_{2}} & 0 \\0 & 0 & 0 & {\mathbb{e}}^{{\mathbb{i}\phi}_{3}}\end{bmatrix},{\phi_{k} = {seed}_{k,j}}$is a uniform random variable between 0 and 2π, and D is the 4×4 DFTmatrix

$\left( {{e.g.},{D = \left\{ {D_{m,n},m,{n = 0},{\ldots\mspace{14mu} 3}} \right\}},{D_{m,n} = {\frac{1}{\sqrt{4}}{\mathbb{e}}^{{j2\pi}\; m\;{n/4}}}}} \right).$

Cluster 1. In an aspect, BeamIndex=36 to BeamIndex=49: If the BeamIndexis equal to j, define seed_(k,j)=(2π[BIT_REVERSE([2*j+k)*26544357611]mod 2³²)] mod 2²⁰)/2²⁰, k=0,1. The corresponding precoding matrix isdefined as BeamMat(:,0:1)*U_(j), where BeamMat(:,0:1) is the zero^(th)and first columns of BeamMat,

${U_{j} = {\Lambda_{j}D}},{\Lambda_{j} = \begin{bmatrix}{\mathbb{e}}^{{j\phi}_{0}} & 0 \\0 & {\mathbb{e}}^{{j\phi}_{1}}\end{bmatrix}},{\phi_{k} = {seed}_{k,j}}$is a uniform random variable between 0 and 2π, and D is a 2×2 DFT matrix(e.g.,

$\left. {{D = \left\{ {D_{m,n},m,{n = 0},1} \right\}},{D_{m,n} = {\frac{1}{\sqrt{2}}{\mathbb{e}}^{{j2\pi}\; m\;{n/2}}}}} \right).$

Cluster 2. In an aspect, BeamIndex=50 to BeamIndex=63: If the BeamIndexis equal to j, define seed_(k,j)=(2π[BIT_REVERSE([(2*j+k)*2654435761]mod 2³²)] mod 2²⁰)/2²⁰, k=0,1. The corresponding precoding matrix isdefined as BeamMat(:,2:3)*U_(j), where BeamMat(:,2:3) is the second andthird columns of BeamMat,

${U_{j} = {\Lambda_{j}D}},{\Lambda_{j} = \begin{bmatrix}{\mathbb{e}}^{{j\phi}_{0}} & 0 \\0 & {\mathbb{e}}^{{j\phi}_{1}}\end{bmatrix}},{\phi_{k} = {seed}_{k,j}}$is a uniform random variable between 0 and 2π, and D is a 2×2 DFT matrix(e.g.,

$\left. {{D = \left\{ {D_{m,n},m,{n = 0},1} \right\}},{D_{m,n} = {\frac{1}{\sqrt{2}}{\mathbb{e}}^{{j2\pi}\; m\;{n/2}}}}} \right).$It is to be appreciated that the foregoing is provided as one or moreexamples; however, the claimed subject matter is not so limited.

Referring to FIGS. 4-6, methodologies relating to constructing unitarymatrices that may be utilized in linear precoding for MIMO systems areillustrated. While, for purposes of simplicity of explanation, themethodologies are shown and described as a series of acts, it is to beunderstood and appreciated that the methodologies are not limited by theorder of acts, as some acts may, in accordance with one or moreembodiments, occur in different orders and/or concurrently with otheracts from that shown and described herein. For example, those skilled inthe art will understand and appreciate that a methodology couldalternatively be represented as a series of interrelated states orevents, such as in a state diagram. Moreover, not all illustrated actsmay be required to implement a methodology in accordance with one ormore embodiments.

With reference to FIG. 4, illustrated is a methodology 400 thatfacilitates yielding one or more unitary matrices that may be utilizedin linear precoding in a MIMO wireless communication system. At 402, adiagonal matrix may be obtained. For instance, the diagonal matrix maybe associated with a random phase. Moreover, the diagonal matrix may besubstantially any size (e.g., substantially any number of columns androws). Further, the diagonal matrix may be generated (e.g., by acommunications apparatus that obtains the diagonal matrix), receivedfrom a disparate source, and so forth. At 404, a DFT matrix may beobtained. The DFT matrix may be a M_(T)×L matrix, where M_(T) may be anumber of transmit antennas and L may be a rank and/or number ofspace-time codes (e.g., spatial multiplexing streams). The DFT matrixmay be generated, received from a disparate source, and the like. At406, a unitary matrix employed in linear precoding may be constructedbased upon the diagonal matrix and the DFT matrix. For example, thediagonal matrix may be multiplied by the DFT matrix to yield the unitarymatrix. Further, the unitary matrix as constructed may enabletransmission power of each transmit antenna (e.g., employing the unitarymatrix) to be substantially equal regardless of a number of streamstransmitted.

Now turning to FIG. 5, illustrated is a methodology 500 that facilitatesproviding channel related feedback by leveraging a set of constructedunitary matrices in a MIMO wireless communication system. At 502, a setof unitary matrices may be constructed, where each of the unitarymatrices in the set may be generated based upon a diagonal matrix and aDFT matrix. For example, a set of N unitary matrices may be generated,where N may be substantially any integer. Moreover, M bits of feedbackmay be utilized to index the unitary matrices, where N=2^(M). Pursuantto another example, each of the unitary matrices may be generated bymultiplying the diagonal matrix by the DFT matrix. At 504, a forwardlink channel may be estimated. For example, eigen decomposition may beeffectuated to yield a channel related unitary matrix. At 506, aparticular unitary matrix from the set of unitary matrices may beselected based upon the estimate of the forward link channel. Accordingto an example, the particular unitary matrix may be selected bycomparing the channel related unitary matrix to the unitary matrices inthe set. For instance, a closest unitary matrix to the channel relatedunitary matrix may be selected; however, the claimed subject matter isnot so limited. At 508, an index of the particular unitary matrixselected from the set of unitary matrices may be determined. At 510, theindex may be transmitted via a reverse link channel. In accordance withan example, a base station and a mobile device may have a commonunderstanding of the index; thus, the base station may employ thetransmitted index to alter subsequent transmission over the forward linkchannel.

Referring to FIG. 6, illustrated is a methodology 600 that facilitatescontrolling transmission over a forward link channel based upon aunitary matrix in a MIMO wireless communication system. At 602, a set ofunitary matrices may be constructed, where each of the unitary matricesmay be generated based upon a diagonal matrix and a DFT matrix. Forexample, the unitary matrix may be multiplied by the DFT matrix. At 604,an index associated with a selected unitary matrix from the set ofunitary matrices may be received. For example, the index may be receivedvia a reverse link channel from a mobile device that utilizes asubstantially similar set of unitary matrices. At 606, the selectedunitary matrix may be identified based upon the index. At 608,transmission over the forward link channel may be modified based uponthe selected unitary matrix. For example, the unitary matrix may bemultiplied by a transmit vector to yield a signal to transmit via theforward link channel.

It will be appreciated that, in accordance with one or more aspectsdescribed herein, inferences can be made regarding providing channelrelated feedback, evaluating channel related feedback, utilizing channelrelated feedback, etc. As used herein, the term to “infer” or“inference” refers generally to the process of reasoning about orinferring states of the system, environment, and/or user from a set ofobservations as captured via events and/or data. Inference can beemployed to identify a specific context or action, or can generate aprobability distribution over states, for example. The inference can beprobabilistic—that is, the computation of a probability distributionover states of interest based on a consideration of data and events.Inference can also refer to techniques employed for composinghigher-level events from a set of events and/or data. Such inferenceresults in the construction of new events or actions from a set ofobserved events and/or stored event data, whether or not the events arecorrelated in close temporal proximity, and whether the events and datacome from one or several event and data sources.

According to an example, one or more methods presented above can includemaking inferences pertaining to selecting a unitary matrix that may beutilized to provide feedback related to a channel from a set of unitarymatrices. By way of further illustration, an inference may be maderelated to determining a unitary matrix to utilize in connection withmodifying transmission over a forward link channel. It will beappreciated that the foregoing examples are illustrative in nature andare not intended to limit the number of inferences that can be made orthe manner in which such inferences are made in conjunction with thevarious embodiments and/or methods described herein.

FIG. 7 is an illustration of a mobile device 700 that facilitatesgenerating a set of unitary matrices that may be employed in linearprecoding for a MIMO wireless communication system. Mobile device 700comprises a receiver 702 that receives a signal from, for instance, areceive antenna (not shown), and performs typical actions thereon (e.g.,filters, amplifies, downconverts, etc.) the received signal anddigitizes the conditioned signal to obtain samples. Receiver 702 can be,for example, an MMSE receiver, and can comprise a demodulator 704 thatcan demodulate received symbols and provide them to a processor 706 forchannel estimation. Processor 706 can be a processor dedicated toanalyzing information received by receiver 702 and/or generatinginformation for transmission by a transmitter 716, a processor thatcontrols one or more components of mobile device 700, and/or a processorthat both analyzes information received by receiver 702, generatesinformation for transmission by transmitter 716, and controls one ormore components of mobile device 700.

Mobile device 700 can additionally comprise memory 708 that isoperatively coupled to processor 706 and that may store data to betransmitted, received data, information related to available channels,data associated with analyzed signal and/or interference strength,information related to an assigned channel, power, rate, or the like,and any other suitable information for estimating a channel andcommunicating via the channel. Memory 708 can additionally storeprotocols and/or algorithms associated with estimating and/or utilizinga channel (e.g., performance based, capacity based, etc.).

It will be appreciated that the data store (e.g., memory 708) describedherein can be either volatile memory or nonvolatile memory, or caninclude both volatile and nonvolatile memory. By way of illustration,and not limitation, nonvolatile memory can include read only memory(ROM), programmable ROM (PROM), electrically programmable ROM (EPROM),electrically erasable PROM (EEPROM), or flash memory. Volatile memorycan include random access memory (RAM), which acts as external cachememory. By way of illustration and not limitation, RAM is available inmany forms such as synchronous RAM (SRAM), dynamic RAM (DRAM),synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhancedSDRAM (ESDRAM), Synchlink DRAM (SLDRAM), and direct Rambus RAM (DRRAM).The memory 708 of the subject systems and methods is intended tocomprise, without being limited to, these and any other suitable typesof memory.

Receiver 702 is further operatively coupled to a unitary matrixgenerator 710 that constructs unitary matrices that can be utilized inlinear precoding. For instance, unitary matrix generator 710 maygenerate a unitary matrix based upon a diagonal matrix and a DFT matrix.Pursuant to an example, unitary matrix generator 710 may multiply thediagonal matrix by the DFT matrix to yield the unitary matrix. Moreover,the diagonal matrix may be associated with a random phase. Further, theDFT matrix may be a M_(T)×L matrix, where M_(T) may be a number oftransmit antennas and L may be a rank and/or number of space-time codes(e.g., spatial multiplexing streams). Additionally, a feedback generator712 may utilize the unitary matrices to provide feedback related to aforward link channel. Feedback generator 712 (and/or a disparatecomponent) may estimate the forward link channel. Moreover, based uponthe estimated forward link channel, feedback generator 712 may select aparticular unitary matrix from the unitary matrices. For instance, anindex associated with the selected unitary matrix may be determined byfeedback generator 712, and thereafter, the index may be transmitted asfeedback over a reverse link channel. Mobile device 700 still furthercomprises a modulator 714 and a transmitter 716 that transmits thesignal to, for instance, a base station, another mobile device, etc.Although depicted as being separate from the processor 706, it is to beappreciated that unitary matrix generator 710, feedback generator 712and/or modulator 714 may be part of processor 706 or a number ofprocessors (not shown).

FIG. 8 is an illustration of a system 800 that facilitates generatingunitary matrices and/or utilizing unitary matrices constructed based atleast in part upon randomized DFT matrices in connection with linearprecoding in a MIMO wireless communication system. System 800 comprisesa base station 802 (e.g., access point, . . . ) with a receiver 810 thatreceives signal(s) from one or more mobile devices 804 through aplurality of receive antennas 806, and a transmitter 822 that transmitsto the one or more mobile devices 804 through a transmit antenna 808.Receiver 810 can receive information from receive antennas 806 and isoperatively associated with a demodulator 812 that demodulates receivedinformation. Demodulated symbols are analyzed by a processor 814 thatcan be similar to the processor described above with regard to FIG. 7,and which is coupled to a memory 816 that stores information related toestimating a signal (e.g., pilot) strength and/or interference strength,data to be transmitted to or received from mobile device(s) 804 (or adisparate base station (not shown)), and/or any other suitableinformation related to performing the various actions and functions setforth herein. Processor 814 is further coupled to a unitary matrixgenerator 818 that constructs unitary matrices based at least in partupon randomized DFT matrices. For example, unitary matrix generator 818may generate a set of unitary matrices that may be substantially similarto a set of unitary matrices utilized by mobile device(s) 804 inconnection with yielding feedback related to a channel obtained by basestation 802.

Unitary matrix generator 818 may be further coupled to a feedbackevaluator 820 that analyzes feedback received via reverse linkchannel(s) from mobile device(s) 804. For example, feedback evaluator820 may obtain an index related to a selected unitary matrix included inthe set of unitary matrices constructed by unitary matrix generator 818.Thus, feedback evaluator 820 may identify the selected unitary matrix.Further, feedback evaluator 820 may effectuate utilizing the selectedunitary matrix in connection with subsequent transmission over a forwardlink channel. Information utilized to control subsequent transmission(e.g., information associated with the selected unitary matrix, theselected unitary matrix combined with a transmit vector, . . . ) may beprovided to a modulator 822. Modulator 822 can multiplex the controlinformation for transmission by a transmitter 826 through antenna 808 tomobile device(s) 804. Although depicted as being separate from theprocessor 814, it is to be appreciated that implicit feedback evaluator818, explicit feedback evaluator 820 and/or modulator 822 may be part ofprocessor 814 or a number of processors (not shown).

FIG. 9 shows an example wireless communication system 900. The wirelesscommunication system 900 depicts one base station 910 and one mobiledevice 950 for sake of brevity. However, it is to be appreciated thatsystem 900 may include more than one base station and/or more than onemobile device, wherein additional base stations and/or mobile devicesmay be substantially similar or different from example base station 910and mobile device 950 described below. In addition, it is to beappreciated that base station 910 and/or mobile device 950 may employthe systems (FIGS. 1-3 and 7-8) and/or methods (FIGS. 4-6) describedherein to facilitate wireless communication there between.

At base station 910, traffic data for a number of data streams isprovided from a data source 912 to a transmit (TX) data processor 914.According to an example, each data stream may be transmitted over arespective antenna. TX data processor 914 formats, codes, andinterleaves the traffic data stream based on a particular coding schemeselected for that data stream to provide coded data.

The coded data for each data stream may be multiplexed with pilot datausing orthogonal frequency division multiplexing (OFDM) techniques.Additionally or alternatively, the pilot symbols can be frequencydivision multiplexed (FDM), time division multiplexed (TDM), or codedivision multiplexed (CDM). The pilot data is typically a known datapattern that is processed in a known manner and may be used at mobiledevice 950 to estimate channel response. The multiplexed pilot and codeddata for each data stream may be modulated (e.g., symbol mapped) basedon a particular modulation scheme (e.g., binary phase-shift keying(BPSK), quadrature phase-shift keying (QPSK), M-phase-shift keying(M-PSK), M-quadrature amplitude modulation (M-QAM), etc.) selected forthat data stream to provide modulation symbols. The data rate, coding,and modulation for each data stream may be determined by instructionsperformed or provided by processor 930.

The modulation symbols for the data streams may be provided to a TX MIMOprocessor 920, which may further process the modulation symbols (e.g.,for OFDM). TX MIMO processor 920 then provides N_(T) modulation symbolstreams to N_(T) transmitters (TMTR) 922 a through 922 t. In variousembodiments, TX MIMO processor 920 applies beamforming weights to thesymbols of the data streams and to the antenna from which the symbol isbeing transmitted.

Each transmitter 922 receives and processes a respective symbol streamto provide one or more analog signals, and further conditions (e.g.,amplifies, filters, and upconverts) the analog signals to provide amodulated signal suitable for transmission over the MIMO channel.Further, N_(T) modulated signals from transmitters 922 a through 922 tare transmitted from N_(T) antennas 924 a through 924 t, respectively.

At mobile device 950, the transmitted modulated signals are received byN_(R) antennas 952 a through 952 r and the received signal from eachantenna 952 is provided to a respective receiver (RCVR) 954 a through954 r. Each receiver 954 conditions (e.g., filters, amplifies, anddownconverts) a respective signal, digitizes the conditioned signal toprovide samples, and further processes the samples to provide acorresponding “received” symbol stream.

An RX data processor 960 may receive and process the N_(R) receivedsymbol streams from N_(R) receivers 954 based on a particular receiverprocessing technique to provide N_(T) “detected” symbol streams. RX dataprocessor 960 may demodulate, deinterleave, and decode each detectedsymbol stream to recover the traffic data for the data stream. Theprocessing by RX data processor 960 is complementary to that performedby TX MIMO processor 920 and TX data processor 914 at base station 910.

A processor 970 may periodically determine which precoding matrix toutilize as discussed above. Further, processor 970 may formulate areverse link message comprising a matrix index portion and a rank valueportion.

The reverse link message may comprise various types of informationregarding the communication link and/or the received data stream. Thereverse link message may be processed by a TX data processor 938, whichalso receives traffic data for a number of data streams from a datasource 936, modulated by a modulator 980, conditioned by transmitters954 a through 954 r, and transmitted back to base station 910.

At base station 910, the modulated signals from mobile device 950 arereceived by antennas 924, conditioned by receivers 922, demodulated by ademodulator 940, and processed by a RX data processor 942 to extract thereverse link message transmitted by mobile device 950. Further,processor 930 may process the extracted message to determine whichprecoding matrix to use for determining the beamforming weights.

Processors 930 and 970 may direct (e.g., control, coordinate, manage,etc.) operation at base station 910 and mobile device 950, respectively.Respective processors 930 and 970 can be associated with memory 932 and972 that store program codes and data. Processors 930 and 970 can alsoperform computations to derive frequency and impulse response estimatesfor the uplink and downlink, respectively.

It is to be understood that the embodiments described herein may beimplemented in hardware, software, firmware, middleware, microcode, orany combination thereof. For a hardware implementation, the processingunits may be implemented within one or more application specificintegrated circuits (ASICs), digital signal processors (DSPs), digitalsignal processing devices (DSPDs), programmable logic devices (PLDs),field programmable gate arrays (FPGAs), processors, controllers,micro-controllers, microprocessors, other electronic units designed toperform the functions described herein, or a combination thereof.

When the embodiments are implemented in software, firmware, middlewareor microcode, program code or code segments, they may be stored in amachine-readable medium, such as a storage component. A code segment mayrepresent a procedure, a function, a subprogram, a program, a routine, asubroutine, a module, a software package, a class, or any combination ofinstructions, data structures, or program statements. A code segment maybe coupled to another code segment or a hardware circuit by passingand/or receiving information, data, arguments, parameters, or memorycontents. Information, arguments, parameters, data, etc. may be passed,forwarded, or transmitted using any suitable means including memorysharing, message passing, token passing, network transmission, etc.

For a software implementation, the techniques described herein may beimplemented with modules (e.g., procedures, functions, and so on) thatperform the functions described herein. The software codes may be storedin memory units and executed by processors. The memory unit may beimplemented within the processor or external to the processor, in whichcase it can be communicatively coupled to the processor via variousmeans as is known in the art.

With reference to FIG. 10, illustrated is a system 1000 that generatesunitary matrices and provides channel related feedback by leveraging theunitary matrices in a MIMO wireless communication environment. Forexample, system 1000 may reside at least partially within a mobiledevice. It is to be appreciated that system 1000 is represented asincluding functional blocks, which may be functional blocks thatrepresent functions implemented by a processor, software, or combinationthereof (e.g., firmware). System 1000 includes a logical grouping 1002of electrical components that may act in conjunction. For instance,logical grouping 1002 may include an electrical component forconstructing a set of unitary matrices based upon diagonal matrices andDFT matrices 1004. For example, a diagonal matrix may be combined with(e.g., multiplied by) a DFT matrix to yield a unitary matrix. Further,logical grouping 1002 may comprise an electrical component for selectinga particular unitary matrix from the set of unitary matrices based upona channel estimate 1006. According to an example, a forward link channelmay be estimated, and the channel estimate (and/or a correspondingchannel related unitary matrix) may be compared to the set of unitarymatrices. Moreover, logical grouping 1002 may include an electricalcomponent for transmitting an index associated with the particularunitary matrix via a reverse link channel 1008. Additionally, system1000 may include a memory 1010 that retains instructions for executingfunctions associated with electrical components 1004, 1006, and 1008.While shown as being external to memory 1010, it is to be understoodthat one or more of electrical components 1004, 1006, and 1008 may existwithin memory 1010.

Turning to FIG. 11, illustrated is a system 1100 that constructs unitarymatrices and controls transmission over a channel by employing theunitary matrices in a MIMO wireless communication environment. System1100 may reside within a base station, for instance. As depicted, system1100 includes functional blocks that may represent functions implementedby a processor, software, or combination thereof (e.g., firmware).System 1100 includes a logical grouping 1102 of electrical componentsthat facilitate constructing unitary matrices and controllingtransmission over a channel. Logical grouping 1102 may include anelectrical component for generating a set of unitary matrices based upondiagonal matrices and DFT matrices 1104. Moreover, logical grouping 1102may include an electrical component for identifying a selected unitarymatrix from the set of unitary matrices based upon a received index1106. For example, the index may be obtained from a mobile device thatutilizes a substantially similar set of unitary matrices to yield theindex. Further, logical grouping 1102 may include an electricalcomponent for controlling transmission over a forward link channel basedupon the selected unitary matrix 1108. Additionally, system 1100 mayinclude a memory 1110 that retains instructions for executing functionsassociated with electrical components 1104, 1106, and 1108. While shownas being external to memory 1110, it is to be understood that electricalcomponents 1104, 1106, and 1108 may exist within memory 1110.

What has been described above includes examples of one or moreembodiments. It is, of course, not possible to describe everyconceivable combination of components or methodologies for purposes ofdescribing the aforementioned embodiments, but one of ordinary skill inthe art may recognize that many further combinations and permutations ofvarious embodiments are possible. Accordingly, the described embodimentsare intended to embrace all such alterations, modifications andvariations that fall within the spirit and scope of the appended claims.Furthermore, to the extent that the term “includes” is used in eitherthe detailed description or the claims, such term is intended to beinclusive in a manner similar to the term “comprising” as “comprising”is interpreted when employed as a transitional word in a claim.

What is claimed is:
 1. A method that facilitates providing channelrelated feedback for precoding in a wireless communication system,comprising: using a set of unitary matrices, each of the unitarymatrices being generated by a processor based upon a diagonal matrixassociated with a random phase and a Discrete Fourier Transform (DFT)matrix; selecting a particular unitary matrix from the set of unitarymatrices based upon an estimate, provided by a feedback evaluator, of aforward link channel; and transmitting an index associated with theparticular unitary matrix via a reverse link channel.
 2. The method ofclaim 1, further comprising generating each of the unitary matrices bymultiplying the diagonal matrix by the DFT matrix.
 3. The method ofclaim 1, wherein the DFT matrix is a MT by L matrix, MT is a number oftransmit antennas and L is a rank of space-time codes.
 4. The method ofclaim 1, further comprising evaluating$F_{M_{T} \times L} = {\frac{1}{\sqrt{M_{T}}}\left\lbrack {\mathbb{e}}^{\frac{{- j}\; 2\;\pi\; n\; l}{M_{T}}} \right\rbrack}$to obtain the DFT matrix, where n is from 0 to MT−1, l is from 0 to L−1,MT is a number of transmit antennas and L is a rank of space-time codes.5. The method of claim 1, wherein columns of the DFT matrix areorthonormal.
 6. The method of claim 1, further comprising transmittingthe set of unitary matrices to a disparate communications apparatus. 7.The method of claim 1, further comprising estimating the forward linkchannel to yield a channel matrix.
 8. The method of claim 7, furthercomprising effectuating eigen decomposition of the channel matrix togenerate a channel unitary matrix.
 9. The method of claim 8, selectingthe particular unitary matrix further comprises comparing the channelunitary matrix with the set of unitary matrices to identify theparticular unitary matrix.
 10. The method of claim 1, wherein the set ofunitary matrices is substantially similar to a set of unitary matricesemployed by a base station to which the index is transmitted.
 11. Themethod of claim 1, wherein the wireless communication system is amultiple-input multiple-output (MIMO) system.
 12. The method of claim 1,wherein the wireless communication system is a time division duplex(TDD) system.
 13. The method of claim 1, wherein the wirelesscommunication system is a frequency division duplex (FDD) system.
 14. Awireless communications apparatus, comprising: a memory that retainsinstructions for using a set of unitary matrices, each of the set ofunitary matrices based upon a combination of diagonal matricesassociated with a random phase and Discrete Fourier Transform (DFT)matrices and yielding channel related feedback, for precoding selectedas a particular unitary matrix from the set of unitary matrices basedupon an estimate of a forward link channel; and a processor, coupled tothe memory, configured to execute the instructions retained in memory.15. The wireless communications apparatus of claim 14, wherein thememory further retains instructions for generating the set of unitarymatrices by multiplying the diagonal matrices by the DFT matrices. 16.The wireless communications apparatus of claim 14, wherein the diagonalmatrices each are associated with a random phase and the DFT matriceseach are a MT by L matrix, MT is a number of transmit antennas and L isa rank of space-time codes.
 17. The wireless communications apparatus ofclaim 14, wherein the memory further retains instructions for estimatinga forward link channel to yield a channel estimate, selecting aparticular unitary matrix for the precoding from the set of unitarymatrices based upon the channel estimate, and transmitting an indexassociated with the particular unitary matrix over a reverse linkchannel.
 18. A wireless communications apparatus that generates unitarymatrices and provides channel related feedback for precoding,comprising: means for using a set of unitary matrices, each of the setof unitary matrices being based upon diagonal matrices associated with arandom phase and Discrete Fourier Transform (DFT) matrices; means forselecting a particular unitary matrix from the set of unitary matricesbased upon an estimate of a forward link channel; and means fortransmitting an index associated with the particular unitary matrix viaa reverse link channel.
 19. The wireless communications apparatus ofclaim 18, further comprising means for constructing each of the unitarymatrices by multiplying a particular diagonal matrix by a correspondingDFT matrix.
 20. The wireless communications apparatus of claim 18,further comprising: means for generating the diagonal matrices; andmeans for constructing the DFT matrices.
 21. A non-transitorycomputer-readable medium having stored thereon machine-executableinstructions for: using a set of unitary matrices generated by aprocessor, each of the unitary matrices being based on a function of adiagonal matrix associated with a random phase and a Discrete FourierTransform (DFT) matrix; estimating a forward link channel to yield achannel estimate; identifying a particular unitary matrix from the setof unitary matrices based upon the channel estimate; determining anindex of the particular unitary matrix selected from the set of unitarymatrices; and transmitting the index via a reverse link channel.
 22. Themachine-readable medium of claim 21, the machine-executable instructionsfurther comprise multiplying the diagonal matrix by the DFT matrix toyield each of the unitary matrices.
 23. In a wireless communicationsystem, an apparatus comprising: a processor configured to: use acodebook of unitary matrices, each of the codebook of unitary matricesbeing based upon diagonal matrices associated with a random phase andDiscrete Fourier Transform (DFT) matrices; and determine a particularunitary matrix to feedback for utilization in precoding based upon anevaluation of a forward link channel provided by a feedback evaluator;and send an index associated with the particular unitary matrix to abase station via a reverse link channel.